Exam 6: Random Variables and Discrete Probability Distributions

To find the probability that X is at most 10, you should find the probability that X is 10 or ____________________.

The Poisson probability distribution is a continuous probability distribution.

Which of the following are required conditions for the distribution of a discrete random variable X that can assume values x_i ?

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. {Shopping Outlet Narrative} Use the laws of expected value to calculate the mean of Y from the probability distribution of X .

Gym Visits Let X represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: {Gym Visits Narrative} Find the mean and the standard deviation of Y = 2 X - 1.

Number of Horses The random variable X represents the number of horses per family in a rural area in Iowa, with the probability distribution: p ( x )= 0.05 x , x = 2, 3, 4, 5, or 6. {Number of Horses Narrative} Express the probability distribution in tabular form.

If X has a binomial distribution with n = 4 and p = 0.3, find P ( X = 0).

If the probability of success p remains constant in a binomial distribution, an increase in n will not change the mean.

Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. {Unsafe Levels of Radioactivity Narrative} Find the probability that there will be exactly 3 incidents in a year.

In a(n)____________________ experiment, the probability of a success in an interval is the same for all equal-sized intervals.

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. {Montana Highways Narrative} Find P ( X = 2).

Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. {Unsafe Levels of Radioactivity Narrative} Find the standard deviation of the number of incidents is in one year.

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance. The distance a person rides in a year is an example of a(n)____________________ random variable.

In the notation below, X is the random variable, c is a constant, and V refers to the variance. Which of the following laws of variance is not true?

To find the probability that X is at least 10, you should find the probability that X is 10 or ____________________.

Which of the following is not a characteristic of a binomial experiment?

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. {Montana Highways Narrative} Find the expected number of vehicles that are traveling on Montana highways and exceeding the speed limit.

Number of Motorcycles The probability distribution of a discrete random variable X is shown below, where X represents the number of motorcycles owned by a family. {Number of Motorcycles Narrative} Find the standard deviation of X .

The length of time for which an apartment in a large complex remains vacant is a discrete random variable.

Classified Department Phone Calls A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another. {Classified Department Phone Calls Narrative} Find the probability that the department will receive at least five calls between 2 and 4 P.M. on a particular afternoon.